
where \(\mathcal {M}\)  is an arbitrary finite subset of \(\mathcal {K}\) .
If \( m_{\alpha _{\bf {x}}}(\varepsilon _{\bf {0}})\ne 0\) , then the provious inequalities show that
\(\alpha _{\bf {x}}\in \ell ^1(\mathcal {K})\cap \ell ^2(\mathcal {K})\) , hence \(\pi (\alpha _{\bf {x}})>0\)  (see [1]})
which is a constradiction.
If we now define \(\lbrace \alpha _{\bf {x}}^{\bf {m}}\rbrace _{{\bf {m}}\in \mathcal {K}}\)  by
\(\alpha _{\bf {x}}^{\bf {m}}(\bf {n}):=\left\lbrace \begin{array}{l@{\quad {\mbox{ }}\quad }l}0 & n_i<m_i\hspace{5.69046pt}(1\le i \le d), \\\alpha _{\bf {x}}({\bf {n}})& \mbox{other,} \\\end{array}\right.\) 
